TECHNICAL NOTE DATA QUALITY
INTRODUCTION
1 Estimates in this publication are based on information obtained from occupants of a sample of dwellings, they are subject to sampling variability. That is, they may differ from those estimates that would have been produced if all dwellings had been included in the survey. One measure of the likely difference is given by the standard error (SE), which indicates the extent to which an estimate might have varied by chance because only a sample of dwellings was included. There are about two chances in three (67%) that a sample estimate will differ by less than one SE from the number that would have been obtained if all dwellings had been included, and about 19 chances in 20 (95%) that the difference will be less than two SEs. Another measure of the likely difference is the relative standard error (RSE), which is obtained by expressing the SE as a percentage of the estimate.
2 Due to space limitations, it is impractical to print the SE of each estimate in the publication. Instead, a table of SEs is provided to enable readers to determine the SE for an estimate from the size of that estimate (see table T1). The SE table is derived from a mathematical model, referred to as the 'SE model', which is created using data from a number of past Labour Force Surveys. It should be noted that the SE model only gives an approximate value for the SE for any particular estimate, since there is some minor variation between SEs for different estimates of the same size.
3 The LFS sample size in September 2008 was approximately onethird smaller than the sample size in September 2007. This is due to an 11% sample reduction that was implemented from November 2007 to June 2008 based on the 2006 sample design, and an additional 24% sample reduction implemented in July 2008. In combination, the two sample reductions are expected to increase the standard errors for estimates from the supplementary surveys by approximately 22% at the broad aggregate level, relative to the 2001 sample design (standard errors will vary at lower aggregate levels). Detailed information about the sample reduction is provided in Information Paper: Labour Force Survey Sample Design, Nov 2007 (Second edition) (cat. no. 6269.0).
CALCULATION OF STANDARD ERROR
4 An example of the calculation and the use of SEs in relation to estimates of people is as follows. Table 6 shows the estimated number of employed men at work in the reference week in Australia, whose main location of work in their main job was at their own home, to be 290,200. Since this estimate is between 200,000 and 300,000, table T1 shows that the SE for Australia will lie between 6,400 and 7,600 and can be approximated by interpolation using the following general formula:
5 Therefore, there are about two chances in three that the value that would have been produced if all dwellings had been included in the survey will fall within the range 282,700 to 297,700 and about 19 chances in 20 that the value will fall within the range 275,200 to 305,200. This example is illustrated in the diagram below.
6 In general, the size of the SE increases as the size of the estimate increases. Conversely, the RSE decreases as the size of the estimate increases. Very small estimates are thus subject to such high RSEs that their value for most practical purposes is unreliable. In the tables in this publication, only estimates with RSEs of 25% or less are considered reliable for most purposes. Estimates with RSEs greater than 25% but less than or equal to 50% are preceded by an asterisk (e.g. *3.4) to indicate they are subject to high SEs and should be used with caution. Estimates with RSEs of greater than 50%, preceded by a double asterisk (e.g. **0.3), are considered too unreliable for general use and should only be used to aggregate with other estimates to provide derived estimates with RSEs of less than 25%. Table T2 presents the levels at which estimates have RSEs of 25% and 50%.
MEANS
7 The RSEs of estimates of mean actual hours worked at home in main or second job is obtained by first finding the RSE of the estimate of the total number of people contributing to the mean (see table T1) and then multiplying the resulting number by the following factors:
 mean hours (actually/usually) worked: 0.8
8 The following is an example of the calculation of SEs where the use of a factor is required. Table 15 shows that the estimated mean actual hours worked at home in second job for men in Australia, who did some work at home, was 8.1 hours, and shows that the number of men at work in the reference week who did some work at home in their second job was estimated as 98,000. The SE of 98,000 can be calculated from table T1 (by interpolation) as 4,900. To convert this to an RSE we express the SE as a percentage of the estimate or 4,900/98,000 = 5.0%.
9 The RSE of the estimate of mean actual hours worked at home in second job for men, who did some work at home, is calculated by multiplying this number (5.0%) by the appropriate factor shown in paragraph 7 (in this case 0.8): 5.0 x 0.8 = 4.0%. The SE of this estimate of mean actual hours worked at home in second job for men, who did some work at home, is therefore 4.0% of 8.0, i.e. 0.3 of one hour. Therefore, there are two chances in three that the mean actual hours worked at home in second job for men, who did some work at home, that would have been obtained if all dwellings had been included in the survey would have been within the range 7.7 hours to 8.3 hours, and about 19 chances in 20 that it would have been within the range 7.4 hours to 8.6 hours.
PROPORTIONS AND PERCENTAGES
10 Proportions and percentages formed from the ratio of two estimates are also subject to sampling errors. The size of the error depends on the accuracy of both the numerator and the denominator. A formula to approximate the RSE of a proportion is given below. This formula is only valid when x is a subset of y.
11 Considering the example from the previous page, of the 290,200 employed men at work in the reference week whose main location of work was at their own home, 71,200 or 25% were born overseas. The SE of 71,200 may be calculated by interpolation as 4,300. To convert this to an RSE we express the SE as a percentage of the estimate, or 4,300/71,200 = 6.0%. The SE for 290,200 was calculated previously as 7,500, which converted to an RSE is 7,500/290,200 = 2.6%. Applying the above formula, the RSE of the proportion is:
12 Therefore, the SE for the proportion of employed men at work in the reference week whose main location of work was at their own home who were born overseas is 1.3 percentage points (=(24.5/100)x5.4). Therefore, there are about two chances in three that the proportion of employed men at work in the reference week, whose main location of work was at their own home and were born overseas is between 23.2% and 25.8%, and 19 chances in 20 that the proportion is within the range 21.9% to 27.1%.
DIFFERENCES
13 Published estimates may also be used to calculate the difference between two survey estimates (of numbers or percentages). Such an estimate is subject to sampling error. The sampling error of the difference between two estimates depends on their SEs and the relationship (correlation) between them. An approximate SE of the difference between two estimates (xy) may be calculated by the following formula:
14 While this formula will only be exact for differences between separate and uncorrelated characteristics or subpopulations, it is expected to provide a good approximation for all differences likely to be of interest in this publication.
STANDARD ERRORS
t1 standard errors of estimates 

         Aust. 
 NSW  Vic.  Qld  SA  WA  Tas.  NT  ACT  SE  RSE 
Size of estimate (persons)  no.  no.  no.  no.  no.  no.  no.  no.  no.  % 

100  340  330  250  200  250  130  90  120  120  120.0 
200  450  430  370  270  330  180  140  190  220  110.0 
300  540  510  450  320  390  220  170  240  300  100.0 
500  660  620  570  390  480  270  220  310  440  88.0 
700  760  710  670  450  550  310  260  350  550  78.6 
1,000  880  810  780  520  630  360  300  380  700  70.0 
1,500  1 030  950  930  600  730  410  350  420  890  59.3 
2,000  1 150  1 060  1 040  670  820  450  390  440  1 050  52.5 
2,500  1 250  1 150  1 150  750  900  500  400  450  1 200  48.0 
3,000  1 350  1 250  1 200  800  950  500  450  500  1 300  43.3 
3,500  1 450  1 300  1 300  800  1 000  550  450  500  1 400  40.0 
4,000  1 500  1 400  1 350  850  1 050  550  500  550  1 500  37.5 
5,000  1 650  1 500  1 450  950  1 150  600  550  600  1 700  34.0 
7,000  1 850  1 700  1 650  1 050  1 300  700  650  650  1 950  27.9 
10,000  2 150  1 950  1 850  1 200  1 500  800  850  800  2 300  23.0 
15,000  2 500  2 250  2 050  1 350  1 700  950  1 150  950  2 650  17.7 
20,000  2 750  2 500  2 250  1 500  1 900  1 150  1 450  1 100  2 950  14.8 
30,000  3 200  2 900  2 600  1 800  2 150  1 450  2 050  1 450  3 350  11.2 
40,000  3 550  3 200  2 850  2 050  2 400  1 700  2 550  1 700  3 650  9.1 
50,000  3 850  3 500  3 150  2 300  2 650  1 950  3 050  1 900  3 900  7.8 
100,000  4 900  4 550  4 300  3 450  3 900  2 750  5 300  2 550  4 900  4.9 
150,000  5 750  5 550  5 300  4 400  5 150  3 300  7 300  2 900  5 700  3.8 
200,000  6 600  6 450  6 200  5 200  6 150  3 700  9 150  3 050  6 400  3.2 
300,000  8 300  8 300  7 850  6 400  7 750  4 200  12 450  3 200  7 600  2.5 
500,000  11 650  11 500  10 600  8 000  9 850  4 850  . .  3 200  9 550  1.9 
1,000,000  17 300  17 500  15 150  10 200  12 600  5 550  . .  . .  13 450  1.3 
2,000,000  23 300  25 850  20 350  12 100  14 550  . .  . .  . .  19 550  1.0 
5,000,000  29 700  41 350  27 450  13 650  15 200  . .  . .  . .  32 600  0.7 
10,000,000  31 800  57 000  32 100  . .  . .  . .  . .  . .  43 500  0.4 
15,000,000  . .  . .  . .  . .  . .  . .  . .  . .  49 100  0.3 

. . not applicable 
T2 levels at which estimates have a standard error of 25% and 50%(a) 

 NSW  Vic.  Qld  SA  WA  Tas.  NT  ACT  Aust. 
 no.  no.  no.  no.  no.  no.  no.  no.  no. 
25% RSE 

Mean hours actually/usually worked at home  5 000  4 300  4 000  2 100  3 000  1 100  600  1 300  5 300 
All other estimates  7 800  6 700  6 300  3 200  4 400  1 700  1 400  1 700  8 600 
50% RSE 

Mean hours actually/usually worked at home  1 600  1 400  1 300  700  1 000  400  100  500  1 200 
All other estimates  2 500  2 200  2 100  1 000  1 400  600  400  700  2 300 

(a) Refers to the number of people contributing to the estimate. 
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